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DURABLE STRUCTURESLNEC Lisbon 31 May - 1June 2012

Life-cycle cost optimization in highway concrete bridges management

Joana Maia de Oliveira Almeida | ESTG-IPVC

Raimundo Moreno Delgado | FEUP-UP

Paulo Fonseca Teixeira | IST-UTL


INDEX

1 2 3 4 5 6

1. Introduction

2. Degradation module

3. Life-cycle cost module

4. Optimization module

5. Application on a set of Portuguese bridges

6. Conclusions

LIFE-CYCLE COST OPTIMIZATION IN HIGHWAY CONCRETE BRIDGES MANAGEMENT

ICDS12 International Conference DURABLE STRUCTURES: from construction to rehabilitation LNEC Lisbon Portugal 31 May - 1 June 2012

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1. INTRODUCTION

A possible approach to support bridge management decisions

The optimization goal is the life-cycle cost minimization (direct and indirect costs).

The main restrictions are concerned with cost and performance limits.

The performance index considered for bridges structures is the state condition,

the one that is periodically classified in bridges inspections

with the usual 5 stages scale (1 for the best conditions and 5 for the worst conditions).

The final objective is to estimate future needs

and identify the optimized plan for interventions

on a set of bridges during a medium/long period of time.

LIFE-CYCLE COST OPTIMIZATION IN HIGHWAY CONCRETE BRIDGES MANAGEMENT1 2 3 4 5 6


1. INTRODUCTION

Methodology structure (module by module)

GENETIC

ALGORITHMIC

OPTIMIZATION

MODULE

DEGRADATION

MODULE

LIFE CYCLE COST

MODULE

INPUT DATA

(Bridges data, Highway data, Cost data, Historical data, restrains, etc)

OUTPUT TO SUPPORT BRIDGE MANAGEMENT DECISIONS

LIFE-CYCLE COST OPTIMIZATION IN HIGHWAY CONCRETE BRIDGES MANAGEMENT1 2 3 4 5 6


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1. INTRODUCTION

Type of interventions and its influence on performance and costs

For each bridge, in each time cycle,

3 different kinds of interventions are considered

to identify the best intervention scenario:

* Adey, B. T.; Hajdin, R.; Methodology for determination of financial needs of gradually deteriorating bridges, Bridge Maint., Safety, Management, Health Monit. and Inf. (2008), Koh & Frangopol (eds).

After repair bridge state conditions (ECf) probabilities, according to the bridge initial state condition (ECi):

1 2 3 4 5 6 LIFE-CYCLE COST OPTIMIZATION IN HIGHWAY CONCRETE BRIDGES MANAGEMENT


2. DEGRADATION MODULE

Probabilistic degradation model based on Markov Matrices

- Orcesi & Cremona Model *

State condition (EC) temporal evolution for different initial state conditions (EC0)

Probability of being in the worst condition (EC5) temporal evolution for different initial states (EC0)

* Orcesi, A. D., Cremona, C. F., Optimization of management strategies applied to the national reinforced concrete bridge stock in France, Structure and Infrastructure Engineering (2009) 355-366.



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2. DEGRADATION MODULE

State condition (EC) temporal evolution for different initial state conditions (EC0)

for unfavorable, normal and favorable conditions

Probability of being in the worst condition (EC5) temporal evolution for different initial states (EC0)

for normal environmental conditions

* Roelfstra, G., Modele d'evolution de l'etat des ponts-routes en beton. PhD thesis, cole Polytechnique Fdral de Lausanne (2001).

Probabilistic degradation model based on Markov Matrices

- Roelfstra Model *



3. LIFE-CYCLE COST MODULE

1 2 3 4 5 6

Direct costs

Indirect costs

Residual values and future costs



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KDECe(p,t),i

Cost coefficient values

Function of the bridge

state condition

CUi,t

Interventions unitary costs

CU1=1000k/m2 (repair)

CU2=1500k/m2 (substitution)

Based on EPs expert knowledge(The median costs associated to a set of repair and substitution interventions, realized during the last decade by EP)

1 2 3 4 5 6

Direct costs

Ap

Bridge deck area

p Bridgee Bridge state conditioni Type of interventiont Time




KIECe(p,t),i

Cost coefficient values

Function of the bridge

state condition

1 2 3 4 5 6

Indirect costs

Dp,c

Days of

intervention


CDT f(TMD, veloc., capacity,..)

Extra time delay cost

16,24/h for light vehicles

42,31/h for heavy vehicles

CDC f(TMD, detour lengh, )

Extra circulation delay cost

0,18/km for light vehicles

0,96/km for heavy vehicles

Kc,i

Traffic

restrictions

on bridge



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Represent the residual value of each scenario

at the end of the analysis period of time

(in relative terms)

Idp,t bridge age

TMDp,t average daily traffic

CU2,t substitution unitary cost

1 2 3 4 5 6

Residual values and future costs




4. OPTIMIZATION MODULE

Classificaodas

Obras

Initial population of individuals (randomly created)

New population generation (selection and reproduction)

X INDIVIDUALS POPULATION

Stop conditions

OPTIMUM SOLUTION (OPTIMUM SCENARIO)

Genetic Algorithm process

1 2 3 4 5 6

X INDIVIDUALS POPULATION

Evaluate the fitness of each individual of the population

Evaluate the fitness of each individual of the population


Individual = intervention scenario


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4. OPTIMIZATION MODULE

Almeida, J. O., Delgado, R. M., Teixeira, P. F. Optimizao das intervenes de conservao num conjunto de Pontes Ferrovirias usando um Algoritmo Gentico, ASCP2011, Coimbra (2011).

Genetic Algorithm calibration *

N of individuals per population:

Depends on the n of bridges

Reproduction operators:

Survival rate 5% - 25%

Crossover rate 75 - 90%

Permutation rate < 10%

Mutation rate 0,1% - 10%



5. APPLICATION ON A SET OF PORTUGUESE BRIDGES

General considerations

Period of time:

5 cycles of 5 years each 25 years

Set of Portuguese bridges:

100 highway concrete bridges

(administrated by EP)

Main characteristics histograms:



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Multi-objective decision support

Direct costs 85% total costs (direct + indirect costs)The indirect costs are not very representative on the total costs

for the rest of the presented analysis results:maximum state condition limit of 3,5 | maximum worth state condition probability of 23%

Better performance

Min

imum

cos

t




Degradation model impact

The degradation model has a big impact in the final results of this kind of analysis.(as it is predictable!)

The environmental conditions are very important whenever they are considered on the model(should be very well characterized for future works, whenever Roelfstra model will be applied)

* used for the rest of the presented analysis results



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Cost coefficients uncertainty and sensitive analysis

Cost coefficients

(function of the bridge state condition)

defined with a probabilistic density triangular law(the tabled coefficients as the most likely valueand a variation of +/-20% of that value)

Final life cycle cost (k) 200 Monte Carlo simulations results:

Around 5%impact!

Low impact!

(calibration is not so important)

Tabled cost coefficients (yet under calibration):




Unitary costs uncertainty and sensitive analysis

Unitary interventions costs defined with

probabilistic density functions

(based on EP expert knowledge)

Final life cycle cost (k) 500 Monte Carlo simulations results:

Around 10%impact!

However, if there is a bigger uncertainty associated to cost

values, the impact in the final results could

be much higher

(With the mean

values)



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6. CONCLUSIONS

Main conclusions from the application results - in terms of degradation model

It is very important to choose the most suitable degradation model for each bridge, taking in consideration its specific kind of structure.

Bridges environmental conditions characterization has a great importance on the degradation models that considers that parameter as input.

(one of the most important data to define in an accurate way for future analysis)

For future works:- Markov Matrices should be verified and adjusted with Portuguese historical

information.

- The age influence on the Markov matrices should be characterized to consider

the influence of that parameter.



6. CONCLUSIONS

Main conclusions from the application results in terms of costs

The direct costs represent more than 85% of the total costs (direct + indirect costs),so the indirect ones are not very representative.

The variation for the state conditions cost coefficients doesnt represent more than 5% of final results variation, so its calibration would not seem at this stage so relevant.

Although the unitary repair and substitution costs are the parameters with the greatest impact at the final life cycle cost values, the uncertainty considered for those parameters

in the presented application, causes a low variation (around 10%) of the final results.

only slightly more than the difference gathered with an eventual variation of the

annual discount rate from 4 to 5%, which is 6.5% of the final total costs.



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ACKNOWLEDGEMENTS

Estradas de Portugal

Fundao para a Cincia e Tecnologia



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